According to Algorithm 1, the major complexity lies in solving the offloading data allocation of problem (REF ) with fixed time allocation.
From Theorem 2, the main complexity of obtaining the optimal offloading data lies in solving equation (REF ) by using the one-dimension search method with complexity \(\mathcal {O}(NK)\) , where \(K\)  denotes the number of iterations for the one-dimension search method.
As a result, the total complexity of the proposed Algorithm 1 is \(\mathcal {O}(L_{\text{it}}NK)\) , where \(L_{\text{it}}\)  is the number of iterations for iteratively optimizing time allocation and offloading data.
Due to the fact that the dimension of the variables in problem (REF ) is \(3N\) , the complexity of solving
problem (REF ) by using the standard interior point method is
\(\mathcal {O}(L_{\text{ip}}N^3)\)  [1]},
where \(L_{\text{ip}}\)  denotes the number of iterations for the interior point method.
